1. Frequency assignment for satellite communication systems Kata KIATMANAROJ Supervisors: Christian ARTIGUES, Laurent HOUSSIN 1

2. Problem definition Current state of the art Contributions Conclusions and perspectives 2

3. Problem definition 3

4. To assign a limited number of frequencies to as many users as possible within a service area 4

5. Frequency is a limited resource! – Frequency reuse -> co-channel interference – Intra-system interference 5

6. Simplified beam SDMA: Spatial Division Multiple Access 6 j k i

7. To assign a limited number of frequencies to as many users as possible within a service area Frequency is a limited resource! – Frequency reuse -> co-channel interference – Intra-system interference Graph coloring problem – NP-hard 7

8. Interference constraints 8 i j i j k Binary interferenceCumulative interference Acceptable interference threshold Interference coefficients

9. Assignment – Logical boxes (superframes) – Demand = |F|x|T| – No overlapping within the superframe – Overlapping between superframes (simultaneous)  may create interference 9 0 ≤ o ij ≤ 1 1 2

10. Superframe structure 10

11. Frames and satellite beams 11

12. 12

13. Current state of the art 13

14. Distance FAPs – Maximum Service FAP – Minimum Order FAP – Minimum Span FAP – Minimum Interference FAP Solving methods – Exact method – Heuristics and metaheuristics 14

15. Two branches – Inter-system interference – Intra-system interference Inter-system interference – Two or more adjacent satellites – Minimize co-channel interference (multiple carriers) Intra-system interference – Multi-spot beams – Geographical zones assuming the same propagation condition 15

16. Contributions 16

17. Part 1: Single carrier models Part 2: Multiple carrier models Part 3: Industrial application 17

18. Single carrier models 18 K. Kiatmanaroj, C. Artigues, L. Houssin, and F. Messine, Frequency assignment in a SDMA satellite communication system with beam decentring feature, submitted to Computational Optimization and Applications (COA) K. Kiatmanaroj, C. Artigues, L. Houssin, and F. Messine, Frequency allocation in a SDMA satellite communication system with beam moving, IEEE International Conference on Communications (ICC), 2012 K. Kiatmanaroj, C. Artigues, L. Houssin, and F. Messine, Hybrid discrete-continuous optimization for the frequency assignment problem in satellite communication system, IFAC symposium on Information Control in Manufacturing (INCOM), 2012

19. 1 frequency over the total duration Same frequency + located too close -> Interference 3 models (supplied by Thales Alenia Space) 19

20. Model 1 (fixed-beam binary interference) – 40 fixed-beams – 2 frequencies / beam even no user – Interference matrix (binary interference) – Graph coloring: DSAT algorithm -> 4 colors 20 8 frequencies in total

21. Model 2 (fixed-beam varying frequency) – 40 fixed-beams – 8 frequencies (different within the same beam) – Cumulative interference – Greedy vs. ILP 21

22. Model 3 (SDMA-beam varying frequency) – SDMA (beam-centered) – 8 frequencies (different within the same beam) – Cumulative interference – Greedy vs. ILP 22

23. Greedy algorithms – User selection rules – Frequency selection rules 23

24. Greedy algorithms – User selection rules – Frequency selection rules 24

25. Integer Linear Programming (ILP) 25

26. 26 Performance comparison ILP 60 sec

27. 27 ILP performances

28. Continuous optimization 28 * Collaboration with Frédéric Mezzine, IRIT, Toulouse

29. Beam moving algorithm – For each unassigned user Continuously move the interferers’ beams from their center positions Non-linear antenna gain Minimize the move Not violating interference constraints 29

30. 30 i j k x User iGainαiαi Δ ix i + jΔ jx + kΔ kx + x0- Matlab’s solver fmincon

31. 31 i j k x User iGainαiαi Δ ix i↓↓↓↓+ j k x- Matlab’s solver fmincon

32. 32 i j k x User iGainαiαi Δ ix i↓↓↓↓ j k x- Matlab’s solver fmincon

33. 33 i j k x User iGainαiαi Δ ix i↓↓↓↓- j k x- Matlab’s solver fmincon

34. 34 i j k x User iGainαiαi Δ ix i↓↓↓↓ j↓↓↓↓ k↓↓↓↓ x+ Matlab’s solver fmincon

35. 35 Matlab’s solver fmincon k: number of beams to be moved MAXINEG: margin from the interference threshold UTVAR: whether to include user x to the move

36. 36 Matlab’s solver fmincon Parameters: k, MAXINEG, UTVAR

37. 37 Beam moving results with k-MAXINEG-UTVAR = 7-2-0

38. 38 Beam moving results with k-MAXINEG-UTVAR = 7-2-0

39. 39 Closed-loop implementation

40. Greedy algorithm: efficient and fast ILP: optimal but long calculation time Beam moving: performance improvement Column generation for ILP Fast heuristics for continuous problem Non-linear integer programming 40

41. Multiple carrier models 41

42. Binary interference Cumulative interference 42

43. Binary interference – LF: loading factor 43

44. Binary interference – A user as a task or an operation – User demand (frequencies) as processing time – Interference pairs as non-overlapping constraints – Disjunctive scheduling problem without precedence constraints – Max. number of scheduled tasks with a common deadline 44

45. Binary interference – Disjunctive graph and clique – {1,2}, {2,3}, {2,4}, {3,5}, {4,5,6} vs. 7 interference pairs – CP optimizer 45

46. Binary interference 46

47. Binary interference 47

48. Binary interference 48

49. Cumulative interference – Overlapping duration should be considered 49

50. Cumulative interference: ILP1 50

51. Cumulative interference: ILP2 51

52. Cumulative interference: ILP3 52

53. Scheduling (CP) vs. ILP (CPLEX) 53

54. Cumulative interference vs. binary interference 54

55. Cumulative interference vs. binary interference 55

56. FAP as scheduling problem Outperform ILP Cumulative -> Binary interference Pattern-based ILP with column generation Heuristics based on interval graph coloring Local search technique 56

57. Industrial application 57 K. Kiatmanaroj, C. Artigues, L. Houssin, and E. Corbel, Greedy algorithms for time-frequency allocation in a SDMA satellite communication system, International conference on Modeling, Optimization and Simulation (MOSIM), 2012

58. Terminal types – 50 dBW, 45 dBW – Max. 24 Mbps, 10 Mbps Traffic types – Guaranteed, Non-guaranteed User priority level and handling 58

59. Symbol rate - Modulation - Coding scheme (RsModCod) – 16 ModCod – 4 symbol rates (Rs) corr. to 5, 10, 15 and 20 MHz – Support bitrate (Mbps) – Different acceptable interference thresholds (alpha) 59

60. Beam positioning methods – Fixed-beam – SDMA beams 60

61. Greedy algorithms 61

62. Fast Flexible Extensive hierarchical search MI (Minimum Interference) MB (Minimum Bandwidth) No performance guarantee 62

63. Minimum Interference (MI) Superframe 1Superframe 2 63 MI New superframe when the old one is utilized.

64. Minimum Bandwidth (MB) 64 New superframe before increasing bandwidth

65. Experimental results 65

66. Test instances 66

67. Assignment time (seconds) 67 BC longer time than FB BC30 longer than BC25 MI about the same time as MB

68. Number of rejected users 68 Largely depended on demand / BW

69. Highly complex problem and fast calculation time requirement ILP impractical MI: least interference MB: least bandwidth Lower bounds on the number of rejected users Local search heuristics 69

70. Conclusions and further study 70

71. Solved FAP in a satellite communication system Binary and cumulative interference Single, multiple carrier, realistic models Greedy algorithm, ILP, scheduling Hyper-heuristics Non-linear integer programming Column generation Local search: math-heuristics 71

72. Thank you 72

73. Frame structure constraints 73

74. 74

75. User priority level and handling – 0 - 3 – Weighted-Round-Robin ordering 75

76. Uplink power control – After the resource assignment – PCMargin – Overall interference reduction 76

77. NbS (superframe) m-n (bin configurations) y1-y2 (low – high frequencies) x1-x2 (leftmost – rightmost time bin) Interference calculation repeats * Use control parameters to limit the search space 77

78. Number of optima for ILPs 78

79. Frequency utilization (MHz) 79 Note: system maximum bandwidth 300 MHz

80. Total interference gap 80